Audio-language retrieval faces a fundamental challenge due to many-to-one mappings, where multiple audio instances correspond to the same or similar textual descriptions. This ambiguity leads to overlapping representations, making it difficult for models to learn discriminative features between samples. Queue-based contrastive learning helps mitigate this ambiguity by maintaining a large pool of negatives, improving retrieval performance. However, selecting appropriate hyperparameters, such as the queue size for optimal performance and the number of epochs to prevent overfitting, remains a challenge. In this study, we propose a LAtent Space Embedding Rank (LASER) analysis. Specifically, we analyze that a low-rank property of a queue indicates the presence of informative negative samples, and demonstrate that the best performance is achieved when the queue has the lowest rank. Furthermore, the convergence of rank variation can be interpreted as the model parameters reaching an optimal state during training. Thanks to the proposed rank-based analysis, the model hyperparameters can be selected analytically rather than through trial and error. Experimental results confirm that retrieval performance depends on queue rank, with lower ranks yielding better performance. These findings suggest that our LASER analysis can provide insight into how rank-based analysis can improve retrieval performance in audio-language tasks.

There has been growing interest in audio-language retrieval research, where the objective is to establish the correlation between audio and text modalities. However, most audio-text paired datasets often lack rich expression of the text data compared to the audio samples. One of the significant challenges facing audio-text datasets is the presence of similar or identical captions despite different audio samples. Therefore, under many-to-one mapping conditions, audio-text datasets lead to poor performance of retrieval tasks. In this paper, we propose a novel approach to tackle the data imbalance problem in audio-language retrieval task. To overcome the limitation, we introduce a method that employs a distance sampling-based paraphraser leveraging ChatGPT, utilizing distance function to generate a controllable distribution of manipulated text data. For a set of sentences with the same context, the distance is used to calculate a degree of manipulation for any two sentences, and ChatGPT's few-shot prompting is performed using a text cluster with a similar distance defined by the Jaccard similarity. Therefore, ChatGPT, when applied to few-shot prompting with text clusters, can adjust the diversity of the manipulated text based on the distance. The proposed approach is shown to significantly enhance performance in audio-text retrieval, outperforming conventional text augmentation techniques.

Conebeam CT using a circular trajectory is quite often used for various applications due to its relative simple geometry. For conebeam geometry, Feldkamp, Davis and Kress algorithm is regarded as the standard reconstruction method, but this algorithm suffers from so-called conebeam artifacts as the cone angle increases. Various model-based iterative reconstruction methods have been developed to reduce the cone-beam artifacts, but these algorithms usually require multiple applications of computational expensive forward and backprojections. In this paper, we develop a novel deep learning approach for accurate conebeam artifact removal. In particular, our deep network, designed on the differentiated backprojection domain, performs a data-driven inversion of an ill-posed deconvolution problem associated with the Hilbert transform. The reconstruction results along the coronal and sagittal directions are then combined using a spectral blending technique to minimize the spectral leakage. Experimental results under various conditions confirmed that our method generalizes well and outperforms the existing iterative methods despite significantly reduced runtime complexity.

The annihilating filter-based low-rank Hankel matrix approach (ALOHA) is one of the state-of-the-art compressed sensing approaches that directly interpolates the missing k -space data using low-rank Hankel matrix completion. The success of ALOHA is due to the concise signal representation in the k -space domain, thanks to the duality between structured low-rankness in the k -space domain and the image domain sparsity. Inspired by the recent mathematical discovery that links convolutional neural networks to Hankel matrix decomposition using data-driven framelet basis, here we propose a fully data-driven deep learning algorithm for k -space interpolation. Our network can be also easily applied to non-Cartesian k -space trajectories by simply adding an additional regridding layer. Extensive numerical experiments show that the proposed deep learning method consistently outperforms the existing image-domain deep learning approaches.

Recently, deep learning approaches with various network architectures have achieved significant performance improvement over existing iterative reconstruction methods in various imaging problems. However, it is still unclear why these deep learning architectures work for specific inverse problems. Moreover, in contrast to the usual evolution of signal processing theory around the classical theories, the link between deep learning and the classical signal processing approaches, such as wavelets, nonlocal processing, and compressed sensing, are not yet well understood. To address these issues, here we show that the long-sought missing link is the convolution framelets for representing a signal by convolving local and nonlocal bases. The convolution framelets were originally developed to generalize the theory of low-rank Hankel matrix approaches for inverse problems, and this paper further extends this idea so as to obtain a deep neural network using multilayer convolution framelets with perfect reconstruction (PR) under rectified linear unit (ReLU) nonlinearity. Our analysis also shows that the popular deep network components such as residual blocks, redundant filter channels, and concatenated ReLU (CReLU) do indeed help to achieve PR, while the pooling and unpooling layers should be augmented with high-pass branches to meet the PR condition. Moreover, by changing the number of filter channels and bias, we can control the shrinkage behaviors of the neural network. This discovery reveals the limitations of many existing deep learning architectures for inverse problems, and leads us to propose a novel theory for a deep convolutional framelet neural network. Using numerical experiments with various inverse problems, we demonstrate that our deep convolutional framelets network shows consistent improvement over existing deep architectures. This discovery suggests that the success of deep learning stems not from a magical black box, but rather from the power of a novel signal representation using a nonlocal basis combined with a data-driven local basis, which is indeed a natural extension of classical signal processing theory.

X-ray computed tomography (CT) using sparse projection views is a recent approach to reduce the radiation dose. However, due to the insufficient projection views, an analytic reconstruction approach using the filtered back projection (FBP) produces severe streaking artifacts. Recently, deep learning approaches using large receptive field neural networks such as U-Net have demonstrated impressive performance for sparse-view CT reconstruction. However, theoretical justification is still lacking. Inspired by the recent theory of deep convolutional framelets, the main goal of this paper is, therefore, to reveal the limitation of U-Net and propose new multi-resolution deep learning schemes. In particular, we show that the alternative U-Net variants such as dual frame and tight frame U-Nets satisfy the so-called frame condition which makes them better for effective recovery of high frequency edges in sparse-view CT. Using extensive experiments with real patient data set, we demonstrate that the new network architectures provide better reconstruction performance.

To address the classic interior tomography problem where projections at each view extend only to the shadow of a circular region completely interior to the subject being scanned, previously we showed that the exact recovery of two- and three-dimensional piecewise smooth images is guaranteed using a one-dimensional generalized total variation seminorm penalty which allows a much faster reconstruction. To further accelerate the algorithm up to a level for clinical use, this paper proposes a novel multiscale reconstruction method by exploiting the Bedrosian identity of the Hilbert transform. More specifically, we show that the high frequency parts of the one-dimensional signals can be quickly recovered analytically with the Hilbert transform because of the Bedrosian identity. This implies that computationally expensive iterative reconstruction need only be applied to low resolution images in the downsampled domain, which significantly reduces the computational burden. Moreover, even for incomplete trajectories such as circular cone-beam geometry, we demonstrate that the proposed multiscale interior tomography approach can be combined with a novel spectral blending method in order to mitigate cone-beam artifacts from missing frequency regions. We show the efficacy of the proposed multiscale algorithm using circular fan-beam, helical cone-beam data, and circular cone-beam geometry. With a graphics processing unit implementation, we demonstrate that the speed of the algorithm can be significantly accelerated up to the level for clinical use for various acquisition geometries.